Radial density and heat fluxes description in the velocity space: Nonlinear simulations and quasi-linear calculations

Médina, J.; Lesur, Maxime; Gravier, Etienne; Réveillé, T.; Idouakass, Malik; Drouot, Thomas; Bertrand, Pierre; Cartier-Michaud, Thomas; Garbet, X.; Diamond, P. H.

doi:10.1063/1.5057420

Cited by 4 publications

(6 citation statements)

References 30 publications

(35 reference statements)

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“…The maximum discrepancy is about equal to 15%. This result is not totally surprising considering the fact that nonlinear simulations and quasi-linear predictions are not always similar [34] for the TERESA model.…”

Section: B Trapped Ion Mode Casementioning

confidence: 73%

Diffusive impurity transport driven by trapped particle turbulence in tokamak plasmas

et al. 2019

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The diffusive impurity transport as a function of the charge and mass numbers is investigated in an ion driven or an electron driven turbulence, in the limit of zero impurity temperature gradient. It is found that the impurity transport decreases slightly with increasing mass number, and depends much strongly on the charge number. Moreover, this transport depends on the nature of the instability that drives turbulence. The impurity flux due to Trapped Electron Mode (TEM) turbulence increases with the charge number Z. In contrast, it is found to decrease with Z in the Trapped Ion Mode (TIM) dominated. In order to explain these observations, the quasilinear flux is derived and is compared with results obtained from the nonlinear simulations. Quasi-linear theory qualitatively reproduces the gyro-kinetic numerical observations.

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Section: B Trapped Ion Mode Casementioning

confidence: 73%

Diffusive impurity transport driven by trapped particle turbulence in tokamak plasmas

et al. 2019

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“…The TERESA code [6,7,10,14,19,32,40] is based on a reduced electrostatic gyrokinetic model focusing on trapped particles, where the cyclotron and bounce motions are averaged out. TERESA is not aimed to quantitatively predict transport in existing or futures tokamaks.…”

Section: A a Bounce Averaged Gyrokinetic Modelmentioning

confidence: 99%

“…Here we give a brief explanation of the model. More details on each terms, as well as the normalization, can be found in [31,32].…”

Section: A a Bounce Averaged Gyrokinetic Modelmentioning

confidence: 99%

“…We also impose the electric potential to be 0 at the edges. Imposing such constraints usually create numerical error when approaching the edges, thus we create an artificial diffusion, "buffers", between ψ ∈ [0; 0.15] and ψ ∈ [0.85; 1] [32]. The ion Larmor radius is ρ i = 0.001 and the ion banana width is δ bi = 0.01 which are given in units of ψ, at the thermal velocity, using the approximation of constant orbits.…”

Section: Grid Number Of Grid Points Valuementioning

confidence: 99%

“…It is possible to further reduce the model by averaging out, in addition to the cyclotron motion, the trapped particle bounce (or banana) motion and considering adiabatic passing particles with kinetic trapped ions (from zero to supra-thermal, although non-relativistic, energies), thus focusing on slow phenomena on a time-scale of the toroidal precession of trapped particles with thermal velocity, which is around 10 −2 s. In this work we use the TERESA code [6,7,10,14,19,31,32,40] which is based on this reduced gyrokinetic model and which is less computationally intensive than standard gyrokinetic codes. This axisymmetric, electrostatic code solves the Vlasov equation coupled to the quasi-neutrality constraint, in a 4 dimensional space: 2 spatial variables (α, ψ) and 2 adiabatic invariants κ and E. α = ϕ − qθ is the precession angle with ϕ the toroidal angle, θ the poloidal angle and q the safety factor, taken independent of the radius.…”

Section: Introductionmentioning

confidence: 99%

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Test particle dynamics in low-frequency tokamak turbulence

et al. 2019

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We study the evolution of one million test particles in a turbulent plasma simulation, using the gyrokinetic code TERESA, as a method to get insights on the type of transport governing the plasma. TERESA (Trapped Element REduction in Semi lagrangian Approach) is a collisionless global 4D code which treats the trapped particles kinetically while the passing particles are considered adiabatic. The Vlasov-Poisson system of equations is averaged over the cyclotron and the trapped particle's bounce motion, thus the model focuses on slow phenomena of the order of the toroidal precession motion of the banana orbits.We initialize the test particles, which are de facto "test banana-centers", at a time of the simulation when the plasma is turbulent. We impose an initial temperature and density gradients and only Trapped Ion Mode (TIM) instability can develop in this system.We then calculate the Mean Squared Displacement (MSD) of the test particles as a function of time in order to obtain a random walk diffusion coefficient. We observe that the radial diffusion of the test particles depends on their toroidal precession kinetic energy (E), in such a way that the transport of particles is dominated by a strong, relatively narrow peak at the resonant energies. A radial particle diffusion flux is then calculated and compared to the total radial particle flux accounting for all the transport processes such as diffusion and advection which is obtained directly from the TERESA code. We can thus compare the diffusive contribution to the particle flux against the non-diffusive contributions. Results show that the total flux is essentially diffusive which is consistent with our simulation set-up aiming for "global turbulence". Both fluxes present a peak around a resonance energy E R ≈ 1.74T i between the TIM and the particles. Both thermal and high-energy particles do not contribute significantly to radial transport.

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Particle dynamics in a turbulent electric field

et al. 2023

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Charged particle velocity-space diffusion in a prescribed one-dimensional turbulent electric field is investigated through numerical trajectories in phase-space and compared against quasi-linear theory (QL), including resonance broadening (RB). A Gaussian spectrum electric field of variable amplitude E is studied in conjunction with two plasma dispersion relations, namely, the Langmuir and ion-acoustic dispersion. A first parameter scan shows that RB effects become significant for a Kubo number K of a few percent. A Kubo number scan shows that diffusion increases as a power law of D∝K3∝E3/2 for large Kubo numbers. Moreover, at large Kubo numbers, transport processes include significant diffusion measured at velocities much higher than the resonant region, where QL and RB predict negligible diffusion. For times much larger than the trapped particle flight time τb and the autocorrelation time τ0, the velocity distribution departs from a Gaussian. Nevertheless, measurements show that the variance increases linearly in time, with a Hurst parameter of H∼0.5, where the diffusion scales as K5/2∝E5/4 and K3/2∝E3/4 for small and large Kubo number, respectively.

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Radial density and heat fluxes description in the velocity space: Nonlinear simulations and quasi-linear calculations

Cited by 4 publications

References 30 publications

Diffusive impurity transport driven by trapped particle turbulence in tokamak plasmas

Diffusive impurity transport driven by trapped particle turbulence in tokamak plasmas

Test particle dynamics in low-frequency tokamak turbulence

Particle dynamics in a turbulent electric field

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